Here is a paper that covers the use of the Golden Ratio (phi) in Statistics. Download the PDF by the link in the upper right corner if you are ready for some math, otherwise, just read the abstract on the linked page.
Warning: I'm not up to date on Statistics, I hated that class but can hum the tune poorly
When somebody has data sets of past activity, the numbers can be crunched to find an equation that will "predict" future values from looking at the past values. This is called "curve fitting". When there isn't enough data to find an equation, the golden mean/golden ratio can be used to fudge it.
Often, exponential equations of y
x match a lot of data sets that grow (bacteria, ebola spreading, etc). Usually though, e
x tends to match nature more than phi/Golden Mean does. There are certain circumstances, such as a limited data set (one or two points), can be extrapolated more accurately using the golden mean (phi) than any other constant.
Basically, curve fitting in statistics finds a linear equation or logarithmic equation to attempt to match all data, and show potential future values. Using the Golden Mean is a single subset of those equations that sometimes yields more accurate results since one or two data points aren't enough to create or guess at any higher order equation.